The mechanical properties of biological tissue (e.g. parameters of elasticity) are of high interest for the characterization of the state of the tissue. In medical diagnostic, changes in the elastic properties reveal histological and possibly also pathological changes of tissue. Commonly known are the development of palpable swellings and lumps. In agriculture mechanical tissue properties are also of interest for the evaluation of the quality of meat.
Examination by palpation is inaccurate and insensitive. Elastography has a much better performance in this regard, because it technically measures the elastic tissue properties and visualizes them quantitatively or qualitatively in the form of cross sectional images [1]. In Elastography ultrasound is used, as it is used as an imaging method in medical diagnostics, but in a modified mode. In a series of sequential ultrasonic images even very small displacements and compressions inside the imaged tissue structures can be measured by the evaluation of the images sequences. A mechanical pressure to the tissue leads to a tissue compression and hence areas of different elastic properties will compress differently. The Elastography system will evaluate these compressions by a numerical comparison of the single images of the series. The strain is displayed in an image. The necessary compression of the tissue is applied externally by the transducer or internally by respiration or the heart beat. The compression is very small, usually some fractions of a millimeter in the order of 0.1%. A quantitative control of the pressure used for the compression is important. The pressure is applied in the propagation direction of the ultrasound.
A method for ultrasonic elastography on biological tissue was first described in 1991 by a paper of J. Ophir et al. [1], [2]. Ultrasound images, or more precisely the high-frequency ultrasound echo signals (HF-data) from which the ultrasound images are created in the ultrasound machine, are evaluated such, that the displacement of the tissue between two images under different tissue compression are calculated. Hence, conclusions about the elasticity can be drawn and even a quantitative reconstruction of the elastic modulus is possible.
The HF-echo signals of a compressed tissue area reach the transducer at a time, that depends on the degree of compression of the compressed tissue area. This causes differences in the propagation time of the echo signals due to the tissue compression, which leads to time shifts in corresponding segments of two echo signals that are acquired with a time delay under different compression of the tissue. Consequently, the main task of the evaluation of the HF-echoes (for the calculation of the strain) is the calculation of the time delay (=time shift) from short time intervals of the HF-echo signals. These time shifts between corresponding echo signals are calculated for at least two locations in the tissue or in the form of a two-dimensional image. For the calculation of time shifts the cross-correlation function of the HF-echo data is used. On one hand, the time shift can be found by maximizing the cross-correlation function [1]. On the other hand, the time shift can found using the phase of the correlation function, normally at zero lag [3,4].
After the calculation of the time shifts, the local strain can be computed by forming a gradient at at least one location in the tissue or also in the form of a two-dimensional image using simple linear filters [6] or by forming a difference, and optionally displayed.
All methods for the calculation of time shift use the cross-correlation function of corresponding intervals of the echo signals of the same tissue area under different compressions. The evaluation is time consuming because the integration has to be performed over the entire interval. The method proposed so far can be divided into two groups:
1) cross-correlation methods: methods, that determine the maximum of the cross-correlation function by a complete search or an iteration procedure. For this method the echo signals have to be sampled at a; very high sampling rates to be able to accurately calculate even very small time shifts. Hence, these methods are very time consuming and can not be implemented in real time or online-systems.
2) phase-based methods: methods, that estimate the time shift from the phase of a value of the cross-correlation function of the complex ultrasonic signals (analytic signals or baseband signals). The disadvantage of these methods are possible inaccuracies and the occurrence of ambiguities for large time shifts. Up to now, these ambiguities could only be prevented by additional, time consuming two dimensional pre or post-processing steps.
Due to the disadvantages of the conventional methods, it is not possible to process echo data with sufficiently accuracy to display strain images in real time. In the past it has been shown, that for ultrasonic imaging like the conventional b-mode or the Doppler sonography the real time capability is of fundamental importance for a wide acceptance of these systems. Another problem is, that the changes in the time-of-flight that result from the tissue compression depend on the distance between the tissue area and the transducer. That means, the time shift is not constant and increases monotonously with distance. The non-constant envelope of the echo signals leads to inaccuracies in the calculation of the time shifts, because for the calculation of the displacements an interval of finite length is used. In the past these inaccuracies have been reduced by a logarithmic amplitude compression of the actual HF-echo data [17]. A disadvantage of this techniques is that the phase of the signals change.
[1] Ophir J., Cxc3xa9spedes I., Ponnekanti H., Yazdi Y., Li X.: xe2x80x9cElastography: A quantitative method for imaging the elasticity of biological tissues. Ultrason. Imaging 13, 111-114, 1991
[2] Cxc3xa9spedes I., Ophir J., Ponnekanti H., Maklad N.: Elastography: xe2x80x9cElasticity imaging using ultrasound with application to muscle and breast imaging in vivo.xe2x80x9d Ultrason. Imaging 15, 73-88, 1993
[3] O""Donnell M., Skovoroda A. R., Shapo B. M., Emilianov S. Y.: xe2x80x9cInternal displacement and strain imaging using ultrasonic speckle trackingxe2x80x9d. IEEE Trans. Ultrason., Ferroelect., Freq. Contr, 41, 314-325, Mai 1994
[4] N. A. Cohn, S. Y. Emelianov, M. A. Lubinski, and M. A. O""Donnell, xe2x80x9cAn elasticity microscope. Part I: methods,xe2x80x9d IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp. 1304-1319, 1997
[5] R. W. Schafer, und L. R. Rabiner, xe2x80x9cA digital signal processing approach to interpolation,xe2x80x9d Proc. of the IEEE, vol. 61, pp. 692-702, 1973
[6] F. Kallel, und J. Ophir, xe2x80x9cA least-squares strain estimator for elastography,xe2x80x9d Ultrason. Imaging 19, 195-208, 1997
[7] I. C{acute over (e )}spedes, und J. Ophir, xe2x80x9cReduction of image noise in elastography,xe2x80x9d Ultrason. Imaging, vol. 15, pp. 89-102, 1993
The object of the invention is to develop a method and a system for processing ultrasonic echo data with sufficient speed and accuracy and/or computing precision (e.g. in real time) for determining values of the tissue distention. This method should yield the same accuracy as other cross-correlation methods using a computational efficient signal processing approach.
The object is solved by a method with the features of claim 1 and an apparatus with the features of claim 6. Phase based algorithms use the phase difference between two echo signals as a measure for the time shift. For single-frequency, time-shifted signals, the phase of the cross-correlation function of two complex echo signals (analytical signals) is a linear function of the time shift. At the actual time shift to be determined, the cross-correlation function has a root (zero crossing). The slope corresponds to the oscillation frequency of the single-frequency signal. This relationship can be exploited for calculating the time shift from a phase of the complex correlation function at an arbitrary position. However, due to the ambiguity of the arctan-function, the phase cannot be unambiguously calculated numerically. Furthermore, in pulse echo systems preferably broadband signals are used. For bandwidth-limited signals the above relationship between the time shift and the cross-correlation function is only approximately valid. This fact leads to the problems of inaccuracy and ambiguities of phase-based methods mentioned above.
Both problems (ambiguities and inaccuracies for broad-band signals) can be solved by using iteratively the ultrasound phase of the cross-correlation function for the search of the maximum of the cross-correlation function, i.e. the zero crossing of the phase of the cross-correlation function. The echo data acquired by the transducer are arranged in A-lines according to FIG. 1. The calculation of the time shift is done at different discrete locations in the tissue or at least at one location in the tissue. In elastography the time shift as a function of depth at these discrete points is a monotone function. For each A-line the time shifts are successively calculated beginning with the point closest to the ultrasound transducer and continuing to the deepest point. At the point closest to the ultrasound transducer, the phase of the value of.the cross-correlation function in unique in spite of the ambiguity of the arctan-function, since the time shifts are very small. For the calculation of the time shift at one point or depth, respectively, the following iteration is performed:
1) The iteration starts at the estimated time shift xcfx84, that has been calculated at the point in the same A-line closer to the transducer. For calculating the points closest to the ultrasound transducer, the iteration starts at zero.
2) The phase of the cross-correlation function of the corresponding ultrasonic echo data at the estimated time shift r is calculated (within a xe2x88x92xcfx80 and +xcfx80 band).
Due to the above explanations, the calculated phase is approximately proportional to the distance of the estimated shift xcfx84 to the real time shift. The proportionality factor approximately corresponds to the centroid frequency of the ultrasound transducer. Consequently, the estimation of the time shift X can be improved by converting the remaining phase to a time shift through division by the centroid frequency and changing the present estimate of the time shift accordingly.
Process step 1) assures that the correlation function is always evaluated in the vicinity of the true time shift. And hence, the remaining phase shift can be determined unambiguously in spite of the ambiguity in the arctan-function and converted to a time shift. By a repeated iteration of 2) inaccuracies of the conversion from phase shifts to time shifts for the use of broadband signals can be iteratively minimized.
With this method, the cross-correlation function has to calculated only a few times (less than 10 times) to obtain a sufficiently accurate estimate of a time shift. Hence, the proposed method is iterative in two ways: time shifts are calculated by an iterative use of the calculated time shifts of the same or preceding image points.
Since in elastography very small time shifts have to be estimated, which are frequently smaller than the sampling time, the echo signals have to be suitably interpolated. The proposed method uses, like [3] and [4], complex baseband-shifted signals for the calculation of the cross-correlation function. The echo signals are shifted to the baseband immediately after the echo signals are recorded. Since these have, due to the bandpass limitation of ultrasound echo signals a significantly reduced upper frequency, a computationally efficient linear interpolation between values of the echo signals is sufficient to also compute values of the cross-correlation function of corresponding echo signals with time shifts that are not integer multiples of the scan time
Inaccuracies in the estimated time shifts can be reduced by this method by using a logarithmic amplitude compression of the complex baseband signals, after these have been incremented by one. Using this method the phase of the base band signals remain unchanged. Consequently the logarithmic compression can also be used for phase based methods.
Unlike currently used phase-based methods, the proposed method reaches the same accuracy as the cross-correlation method. Furthermore the cross-correlation function only has to be evaluated a few times (less than 10 times) to accurately calculating the time shift. Consequently, real time processing of the echo signals for the calculation of tissue strains is already possible by using a suitable signal processing unit which is available in modern ultrasonic machines or are otherwise commercially available or can be fabricated in form of digital circuits.